147 © 2025 The Author(s). Published by College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad. This is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 International License Modeling of Moth Eye Structures for Silicon Solar Cells Efficiency Enhancement Ethar S. Jasim 1 , Imad H. Khaleel 2* and Ali F. Al-Shawabkeh 3 1,2Department of Physics, College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq. 3 Department of Scientific Basic Sciences, Faculty of Engineering Technology, Al-Balqa Applied University, Amman, Jordan. *Corresponding Author. Received: 9 June 2024 Accepted:7 October 2024 Published: 20 July 2025 doi.org/10.30526/38.3.4028 Abstract Moth-eye nano-structure is essentially used as a light-trapping technique for more efficient and cost-effective solar cells. This computational study investigated two dimensions of rectangular silicon base anti-reflected nanostructure for ultra-thin film solar silicon cell efficiency enhancement. The introduced simulation procedure depends on numerical methods and Lumerical software. Impacts of the structure geometry, which was the width and height, on optical and electrical properties were investigated. It found that the geometry of the structure has a significant effect on the absorption and reflection spectrum, due to structure light-trapping effects, and the maximum absorption increases in visible regain reported at a width of 300 nm and height of 100 nm. We also determined the fill factor, short circuit current, and open circuit voltage. It is found that the short circuit current density is significantly influenced by the structure geometry due to a change in absorption, which influences electron-hole generation. It’s also found that the performance can be enhanced by choosing a suitable dimension for the suggested structure. The optimum efficiency enhancement achieved was from 8.71% to 11.89%, and the obtained results are encouraging for using the presented procedure to design more complex structures. Keywords: Moth-Eye, Nano structures, Solar cells, Finite difference time domain, Efficiency enhancement. 1. Introduction The world has faced an existential threat due to the continuous population increases and finite natural resources. Conversely, the pollution associated with the increased consumption of fossil energy sources has led to climate change (1-4). Sustainable energy is required to combat these risks, and solar energy is the most promising. Today. silicon solar cells represent 90% of photovoltaic cells because of their high operational stability, nontoxicity, and abundance (5-8). However, getting good absorption throughout a wide range of solar spectrum requires a considerable amount of silicon material with a topical cell thickness of roughly 180-300 µm, https://orcid.org/0009-0005-6672-548X mailto:Ethar.Sarhan2104m@ihcoedu.uobaghdad.edu.iq https://orcid.org/0000-0003-4498-0752 mailto:imad.h.kh@ihcoedu.uobaghdad.edu.iq https://orcid.org/0000-0001-7350-6000 mailto:drshawabkeh@bau.edu.jo https://orcid.org/0009-0005-6672-548X mailto:Ethar.Sarhan2104m@ihcoedu.uobaghdad.edu.iq https://orcid.org/0000-0003-4498-0752 mailto:imad.h.kh@ihcoedu.uobaghdad.edu.iq https://orcid.org/0000-0001-7350-6000 mailto:drshawabkeh@bau.edu.jo https://orcid.org/0009-0005-6672-548X mailto:Ethar.Sarhan2104m@ihcoedu.uobaghdad.edu.iq https://orcid.org/0000-0003-4498-0752 mailto:imad.h.kh@ihcoedu.uobaghdad.edu.iq https://orcid.org/0000-0001-7350-6000 mailto:drshawabkeh@bau.edu.jo https://orcid.org/0009-0005-6672-548X mailto:Ethar.Sarhan2104m@ihcoedu.uobaghdad.edu.iq https://orcid.org/0000-0003-4498-0752 mailto:imad.h.kh@ihcoedu.uobaghdad.edu.iq https://orcid.org/0000-0001-7350-6000 mailto:drshawabkeh@bau.edu.jo https://orcid.org/0009-0005-6672-548X mailto:Ethar.Sarhan2104m@ihcoedu.uobaghdad.edu.iq https://orcid.org/0000-0003-4498-0752 mailto:imad.h.kh@ihcoedu.uobaghdad.edu.iq https://orcid.org/0000-0001-7350-6000 mailto:drshawabkeh@bau.edu.jo https://orcid.org/0009-0005-6672-548X mailto:Ethar.Sarhan2104m@ihcoedu.uobaghdad.edu.iq https://orcid.org/0000-0003-4498-0752 mailto:imad.h.kh@ihcoedu.uobaghdad.edu.iq https://orcid.org/0000-0001-7350-6000 mailto:drshawabkeh@bau.edu.jo https://orcid.org/0009-0005-6672-548X mailto:Ethar.Sarhan2104m@ihcoedu.uobaghdad.edu.iq https://orcid.org/0000-0003-4498-0752 mailto:imad.h.kh@ihcoedu.uobaghdad.edu.iq https://orcid.org/0000-0001-7350-6000 mailto:drshawabkeh@bau.edu.jo https://orcid.org/0009-0005-6672-548X mailto:Ethar.Sarhan2104m@ihcoedu.uobaghdad.edu.iq https://orcid.org/0000-0003-4498-0752 mailto:imad.h.kh@ihcoedu.uobaghdad.edu.iq https://orcid.org/0000-0001-7350-6000 mailto:drshawabkeh@bau.edu.jo IHJPAS. 2025, 38(3) 148 which raises the production cost, so one possible solution to minimize the cost is ultra-thin silicon solar cell with thickness in few micrometers due to needing less material and protection cost and it has a lot of interest recently (9-15). Ultra-Thin Film Solar Cell UTFSC has lower efficiency because of decreasing silicon thickness, and surface, bulk recombination. As a result, both experiential and theoretical work established several light trapping techniques to minimize the reflection on the surface and maximize the absorption of light to enhance the UTFSC efficiency, such as surface texturing, anti-reflected coating, diffraction grating, metallic nanoparticles (16-25). In this study, we establish a computational model based on the FDTD combined with a Lumerical-Charge solution that has been utilized to investigate alternative designs of silicon- based like moth eye nanostructure for lowering solar cell production costs and improved efficiency. 2. Materials and Methods Solar cells' efficiency depends on the design and optical and electrical material properties. For the optical simulation, the absorption of silicon solar cells' active layer per unit volume is defined by (26): | | ( ) (1) where| | is the electric field, is the angular frequency, and ( ) represents a permittivity imaginary part. Dividing absorption energy per unit volume by the energy per photon (ħ ), one can calculate the photon generation rate (27). | | ( ) (2) Where is a reduced Planck's constant. The integration of (g) over the whole spectrum, which is considered in this study ( ) determines the photon generation rate. If we consider an ideal case, the current length unit ( ⁄ ) can be expressed as (28): (3) Where is the charge on an electron Solar cell quantum efficiency can be defined as (29): ( ) ( ) ( ) (4) Where Pin ( ) and Pabs ( ) are the powers of the incident and absorbed photons at a wavelength ( ) respectively. The following equations yield the ideal short-circuit current density ( ) (30): ( ) ∫ ( ) ( ) (5) Where c denotes the speed of light in free space, denote considered solar irradiance. The solar cell open-circuit voltage can be defined as (31): ( ) (6) Where; is the temperature, represents the Boltzmann constant, is the electron charge, is the light saturation current, and is the dark saturation current, and A is the solar ideality factor. The current density can be expressed as (28): IHJPAS. 2025, 38(3) 149 ( ) (7) Where is the generation rate, and and are the electron and hole diffusion lengths, respectively The fill factor gauges a solar cell's J-V properties is given by (32): (8) The output power, or maximum power, can be stated as: (9) Finally, the efficiency of a solar cell can be expressed as (33): ⁄ (10) where It is the incident power. Modeling solar cells as a device requires both optical and electrical simulations. Figure (1.a) represents a two-dimensional schematic diagram for ultra-thin film silicon solar cells with a Moth-Eye nano-structure array, where the front contact (emitter) and rear contact (base) are made of Silver (Ag), and Aluminum (Al), respectively. R represents the external loud. Also, the optical and electrical simulation regions are shown. Figure (1.b) represents the optical simulation diagram established by FDTD simulation. A planer wave light source was employed, and both the reflection and transmitting were monitored by an R-monitor and T- monitor below, and above the solar cell respectively. The left and right are set to be periodic boundary conditions (PBC) meanwhile, the upper and bottom sides are set to be perfectly matched layers (PML). The geometry of moth-eye array units is set to be rectangular where w and h represent the width and height respectively while d represents the distances between two structures, and the material of the structure is silicon. Figure 1. (a) Solar cell with rectangular moth-eye structure, electrical and optical simulation regions. (b) The optical simulation region unites cells. The device simulation was done in three steps as shown in Figure (2), in the first step optical properties (Reflection, Absorption, Transmission), heat, and electrical generation profile within the active region of the silicon solar cell over the entire incident solar spectrum were computed by FDTD-Lumerical software employing Equation (1) and Equation (2), for a given incident planer wave in the study frequency range (300-1100nm), after import optical martial properties for the active region of solar cell and proposed moth-eye structure(34). Further, the ideal circuit current can be calculated using Equation (5). The second step, which represents thermal simulation, the heat generation profile was computed from the first step then the heat energy was calculated from the absorbed photon which has energy above the IHJPAS. 2025, 38(3) 150 bandgap energy of solar active martial. In the third step, the optical and heat generation profile is imported from the last two steps, then a voltage sweep is carried out to obtain current-voltage characteristics and power-voltage curve of the modulated solar cell. So, the open-circuit voltage , current density , fill factor , maximum power , and the solar cell efficiency calculated by employing Equation (6, 7, 8, 9, 10) respectively. Figure 2. Three simulation steps: optical, heat, and electrical. 3. Results and Discussion To study the effects of the suggested moth-eye structure on the silicon solar cell performance, four subwavelength widths were considered for the rectangular structure ( ), and for each width value of the rectangle, there were nine values for the structure height ( ), and the material of the structure chosen to be silicon, so the added material is in homogenous with solar cell active material, and easy to fabricate. Further, the simulation temperature is set to be at room temperature 300 K, and the energy gap of the silicon active region is set to be (1.114eV) (35). 3.1. Optical Simulation Results The effect of adding a rectangular substrate on reflection, absorption, and transmission spectra and prosed structure were noted in Figure (3). It was shown that the transmission in all cases through the suggested solar cell is zero due to the Aluminum metal contact as seen in Figure (1.b). IHJPAS. 2025, 38(3) 151 Figure 3. Reflection, Absorption, and Transmission spectra for different moth-eye structure widths: w= 0, 100, 200, 300, 400, and 500 nm, while the height of the structure was kept constant at h=50nm. Furthermore, the ripples that appear in the absorption and reflection spectrum are caused by the Fabry-Perot resonant effect, which occurs inside a thin film solar cell with a metal base (36-38). It is also revealed from Figure (3) that there is a significant effect of adding structure on the reflection and transmission spectra. For example, in the case w=100nm, absorption increased relative to its initial values (without adding structure), and this absorption enhancement is clearer in the case w=200nm, and w=300nm. However, when the structure widths increased from 300nm to 400 nm, the corresponding absorption decreased. Further, when the structure width increased to 500nm, which means that the surface was covered completely with a silicon structure 50nm thick, the absorption decreased and became the same as the initial case (without adding structure). IHJPAS. 2025, 38(3) 152 Figure (4) represents the variation of absorption in case w=300nm with different values of structure height (h=0, 100, 200, 300, 400 nm). It is seen that the height of the structure has a significant effect on absorption, and the most absorption increase in visible region accords at height was (h=100nm) this absorption increased due to the maximization of the length of the optical path because of multiple reflection processes leading to confinement of the incident photons with the solar cell active layers (39, 40). Figure 4. Absorption spectra for different moth-eye structure widths: w= 100nm, and different heights h= 0, 100, 200, 300, 400 nm. 3.2. Electrical Simulation Results The electrical characteristics of the first suggested solar cell structure (w=100nm) for different structure heights are listed in Table (1), It can be mentioned that the structure height significant effect on the solar cell short circuit current density , due to absorption enhancement, which leads to an increase in generation rate, the short circuit current increases from its initial value 17.19 ⁄ to 19.19 ⁄ at h=50nm, and then to a maximum value 21.42 ⁄ at h=100nm. Meanwhile, value decreases for higher structure height to 150, 200, 250 nm, and so on, due to the absorption decreases under these conditions. The maximum enhancement in current density was reported at a height of 100nm, which achieved about 24.4% of its initial value. Additionally, fill factor and open circuit voltage were slightly changed due to structure height variations, and the maximum value for both was achieved at h=100nm. Further, solar cell efficiency was enhanced from 8.71% to 10.98% at the case h=100nm due to the open circuit voltage, short circuit current, and fill factor. Table 1. The impact of structure height on solar cell performance at structure width w=100nm. High (nm) ( ⁄ ) ( ) FF ( ) 0 17.1892 0.610627 0.829743 8.70914 50 19.191 0.614063 0.828713 9.76597 100 21.4248 0.616381 0.829932 10.9599 150 20.9735 0.61593 0.829458 10.7151 200 20.2093 0.61514 0.882879 10.3032 250 19.3177 0.614246 0.828648 9.83257 300 19.4848 0.614424 0.828664 9.92069 350 19.2034 0.614109 0.828695 9.77279 400 18.7793 0.61332 0.829008 9.54831 450 17.7391 0.611513 0.829565 8.99888 0 0.2 0.4 0.6 0.8 1 0.3 0.5 0.7 0.9 1.1 A b so rp ti o n Wavelength (μm) w=300nm h=0 nm h=100nm h=200nm h=300nm h=400nm IHJPAS. 2025, 38(3) 153 The effect of adding structure width is also investigated, Table (2) lists the short current density, and solar cell efficiency at different widths: 200, 300, and 400nm. It can be seen that there is similar behavior to the case w=100nm, the short circuit current increased gradually to a certain value of height which was h=100nm, and then it decreased after that certain value. As a result, the optimum design for the suggested rectangular structure with 300nm width and 100 nm height achieved an efficiency equal to 11.89 %, which means an efficiency enhancement of about 36.48%. Table 2. The effect of structure height on at structure widths: w=200, 300, 400nm. structure Width w=200nm Width w=300nm Width w=400nm Height h (nm) ( ⁄ ) ( ) ( ⁄ ) ( ) ( ⁄ ) ( ) 0 17.189 8.709 17.189 8.709 17.189 8.709 50 19.632 9.998 19.867 10.122 19.366 9.856 100 22.584 11.588 23.132 11.886 21.886 11.209 150 21.697 11.108 21.664 11.089 20.075 10.233 200 19.832 10.104 19.626 9.996 18.376 9.335 250 18.484 9.392 17.650 8.951 17.342 8.789 300 17.903 9.086 17.417 8.829 16.738 8.470 350 17.566 8.907 16.898 8.555 16.076 8.121 400 17.584 8.917 16.288 8.233 15.782 7.965 450 17.243 8.737 15.402 7.764 15.450 7.790 Figure (5) represents the power density-voltage curves for the suggested four structures, It is clear that the best design (higher output power density) was achieved at (w=100nm) with a maximum output power density of about 11.89 ⁄ which represents an enhancement in the short circuit current density of about 34.57%. Figure 5. The power density-voltage curves for suggested structures. The Current density-voltage characteristics curves for the suggested four structures are represented in Figure (6). The maximum output current density achieved at w=300nm, with a maximum current density of about 23.13 ⁄ 0 1.5 3 4.5 6 7.5 9 10.5 12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 p o w er ( m W /c m 2 ) Voc (Volte) w=100nm w=200nm w=300nm w=400nm IHJPAS. 2025, 38(3) 154 Figure 6. The Current density-voltage characteristics curve for the suggested structures. Figure (7) shows the variation of the efficiency ( ) as a function of the rectangle structure heights (0, 50, 100, 150, 200, 250, 300, 350, 400, 450nm) for the four structures design width (100, 200, 300, 400nm). It is obvious that, in each case, efficiency increases (from its initial value 8.709% ) gradually with increases in structure heights until it reaches its maximum values which are 10.960%, 11.589%, 11.886%, 11.209% respectively at a certain structure height which was (h=100nm), after that the efficiency decreases gradually. Figure 7. The Current density-voltage characteristics curves for suggested structures. In fact, in each rectangle structure, there is an optimum design to achieve maximum improvements in ultra-thin film silicon solar cells, and the optimum improvement is achieved at a width of 300 nm, and 100nm in height. 4. Conclusion This work considered rectangular silicon moth-eye structures with different dimensions to enhance silicon solar cell performance. The optical and electrical simulations show that the geometry of the introduced structure has a significant effect on suggested solar cell performance, with optimum enhancement achieved from 8.709% to 11.886% at a width of 300nm at a height of 100nm, we recommended introducing a more complex structure for additional performance enhancement, and it's helpful in use another optical design programs such as Silvaco, or SCAPS to develop the work in the future. 0 5 10 15 20 25 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Is c (m A /c m 2 ) V (Volte) w=100nm w=200nm w=300nm w=400nm 0 1 2 3 4 5 6 7 8 9 10 11 12 -50 50 150 250 350 450 E ff ic ie n cy % Stracture Hight(nm) w=100nm w=200nm w=300nm w=400nm IHJPAS. 2025, 38(3) 155 Acknowledgment Thanks to the University of Baghdad, College of Education for Pure Science (Ibn Al-Haitham), Department of Physics. Conflict of Interest Not Found. Funding None. References 1. 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